Turbine flowmeter



Oct. 12,1965 H. KARLBY ETAL TURBINE FLOWMETER 8 Sheets-Sheet 1 OriginalFiled Feb. 27, 1958 INVENTORS l /e/vnmva finer BY W% 9W ATTORNEYS Oct.12, 1965 H. KARLBY ETAL 3,210,997

TURBINE FLOWMETER BY 7 W ATTORNEYS Oct. 12, 1965 H. KARLBY ETAL3,210,997

TURBINE FLOWMETER Original Filed Feb. 27, 1958 8 Sheets-Sheet 3 47' w BYW fl ATTORNEYS Oct. 12, 1965 H. KARLBY ETAL 3,210,997

TURBINE FLOWMETER Original Filed Feb. 27, 1958 8 Sheets-Sheet 4ATTORNEYS BY W046,

Oct. 12, 1965 H. KARLBY ETAL 3,210,997

TURBINE FLOWMETER Original Filed Feb. 27. 1958 8 Sheets-Sheet 5ATTORNEYS BY W WW Oct. 12, 1965 H. KARLBY ETAL 3,210,997

TURBINE FLOWMETER Original Filed Feb. 27. 1958 8 Sheets-Sheet 6 3&9 sea304 INVENTORS HEN/mm A1215) BY fl ATTORNEYS United States Patentassignors to Rockwell Manufacturing Company, Pittsburgh, Pa., acorporation of Pennsylvania Original application Feb. 27, 1958, Ser. No.717,863. Divided and this application Feb. 13, 1962, Ser. No.

- 12 Claims. c1. 73 231 This is a division of our copending applicationSerial Number 717,863 filed February 27, 1958 which is acontinuation-in-part of our copending application Serial Number 634,662filed January 17, 1957.

The present invention relates to improvements in fluid meters and moreparticularly to the provision of a high capacity fluid meter operablefor the direct measurement of both steady and fluctuating flow of fluidsover a wide viscosity range with high accuracy, large flow ratio, smallhead loss and at all practical line pressures.

At present, three different basic types of meters are in wide usage forthe measurement of fluid flow: reciprocating and rotary positivedisplacement meters and orifice meters. Reciprocating positivedisplacement type meters are accurate and suited for fluctuating flow,but are rather bulky, expensive and good for low pressure only. Thistype of meter is thus limited to use in measuring low rates of flow.Rotary positive displacement type meters have been accepted as accurateinstruments for measuring medium quantities of fluid at low or moderatepressure. They become intolerably bulky and expensive when designed forlarge rates of floW or high pressure. The orifice meter has been longrecognized as the simplest form of measuring apparatus for medium andlarge quantities of fluid at all practical line pressures. It has theinherent disadvantage of low flow ratio due to the fact that the rate offlow is proportional to the square root of the measured quantities. Itis not a measuring device of high accuracy and is unfitted for meteringfluctuating flow. To obtain the total flow, its chart must'be integratedwith an expensive integrator, a time consuming operation.

From the above considerations, it i apparent that heretofore, there havebeen no satisfactory instruments in general use for the directmeasurement of both steady and fluctuating flow of medium and largerates at moderate and high pressures with high accuracy, large flowratio, and small head loss. The present invention contemplates theprovision of a turbine meter of improved construction which satisfiesthese requirements, and has the ability to drive a mechanical registerwithout an external power source.

Turbine meters, as such, have been known for many years but none, in sofar as We are presently aware, have been of a design which is effectiveto provide an accurate direct measurement of both steady and fluctuatingflow at medium and large rate and moderate and high pressures over alarge flow rate range with small head loss as is essential in anycommercially acceptable turbine meter. Examples of patented prior artturbine meters are disclosed in United States Patent No. 697,492 issuedApril 15, 1902 to W. H. Kelly et al. for Electromagnetic Water Meter;No. 1,463,865 issed August 7, 1923 to R. S. Blair for Fluid Meter;2,593,285 issued April 15, 1952 to C. H. Fayet al. for Oil Well FlowMeter, and No. 2,713,261 issued July 19, 1955 to G. J. Butterworth etal. for Self-Contained Flow Meters.

As will become fully apparent presently, the design criteria andoperating requirements of a turbine meter are vastly different fromthose of a conventional turbine. The purpose of a conventional powerturbine is to convert the kinetic energy of fluid flow into shaft work.

3,210,997 Patented Oct. 12, 1965 Ice It is designed for maximum powerextraction with reasonably high efliciency. The turbine used for themeasurement of fluid flow is, however, one of zero output. In a turbinemeter, mechanical friction losses and flow losses are the only sourcesof power consumption. A commercially acceptable turbine meter must bedesigned to provide a linear relationship between the turbine speed andthe rate of flow, high driving torque for a given slip of the rotor, lowweight and low moment of inertia of rotor assembly, small head loss,large flow ratio, and independence of viscosity effect.

With the foregoing general considerations in view. the basic objects ofthis invention are to provide an improved turbine meter which has:

(a) Linear proportionality between turbine speed and rate of flow withinits operating range;

(b) High driving torque for a given slip of the rotor;

(c) High flow ratio (R =Q /Q where Q,,,,,,, is the rated capacity of themeter and Qmin, is the minimum rate of flow corresponding to certainallowable percentage of error);

(d) Low effective weight of the rotating parts of the turbine tominimize mechanical friction to insure high accuracy especially at lowflow rates, low moment of inertia of the rotating parts to provide quickresponse to fluctuating flow;

(e) A single meter constant for fluids of different viscosities or for awide variation of viscosity due to temperature change;

(f) Low head loss across the meter;

(g) No pulsation and virtually noiseless;

(h) Unrestricted flow passage through the turbine meter, thus adaptableto handling solids in suspension; and

(i) Simplicity of construction and low cost.

These and subsidiary objects of the present invention will become morefully apparent by reference to the appended claims and as the followingdetailed description proceeds in reference to the accompanying drawingswherein:

FIGURE 1 is a top plan view of a turbine fluid meter embodying theprinciples of the present invention, and primarily adapted for meteringgases;

FIGURE 2 is a sectioinal view of the meter in FIG- URE 1 takensubstantially along the line 2-2 of FIG- URE 1;

FIGURE 3 is a sectional view taken substantially along the line 3-3 ofFIGURE 2;

FIGURE 4 is an enlarged fragmentary sectional view illustrating theturbine rotor of the meter of FIGURE 1;

FIGURE 5 is an enlarged fragmentary sectional view illustrating therelation of the turbine rotor blades to the annular flow passage in themeter of FIGURE 1;

FIGURE 6 is a sectional view taken substantially along the line 6-6 ofFIGURE 4;

FIGURE 7 is a perspective view of the turbine rotor and supportstructure therefor of the meter of FIGURE 1;

FIGURE 8 is substantially diametral sectional view of the turbine rotorof the meter of FIGURE 1;

FIGURE 9 is a side elevational View of one of the blades of the rotor ofFIGURE 8;

FIGURE 10 is a top plan view of the blade of FIG- URE 9;

FIGURE 11 is a development of a fragmentary cylindrical section of thetips of the blades of the rotor of FIGURE 8;

FIGURE 12 is'a development of a fragmentary cylindrical section at theroots of the blades of the rotor of FIGURE 8;

FIGURE 13 is a fragmentary longitudinal section through the registerdrive train and magnetic coupling of the meter of FIGURE 1;

3 FIGURE 14 .is a left end view of the assembly of FIG- URE 13;

FIGURE 15 is a view similar to FIGURE 4 of an enlarged and modified formof the meter of FIGURE 1 primarily adapted for use in metering liquids;

FIGURE 16 is a top plan view of one of the blades of the rotor of FIGURE15 illustrating the twisted blade construction;

FIGURE 17 is a development of a fragmentary cylindrical section at thetips of the blades of the rotor of FIGURE 15;

FIGURE 18 is a development of a fragmentary cylindrical section at theroots of the blades of the rotor of FIGURE 15 FIGURE 19 is adiagrammatic illustration of a longitudinal sectional view through aturbine meter;

FIGURE 20 is a transverse sectional view through the turbine meter ofFIGURE 19 taken substantially on the line 20-20 of FIGURE 19;

FIGURE 21 is a velocity diagram at starting condition of an axial-flowturbine meter as illustrated in FIG URE 19;

FIGURES 22 and 23 are a velocity diagram at syn chronous speed of theturbine meter of FIGURE 19;

FIGURE 24 is a graph illustrating the transient response of the turbinemeter to an instantaneous change in flow rate; and

FIGURES 25 and 26 are a graph showing the transient error of a turbinemeter as a function of the nature of the pulsating flow.

This disclosure of the present invention will proceed with a detaileddescription of the structural arrangement of the disclosed embodiment ofthe present invention, a mathematical analysis of the operation ofturbine meters and a detailed explanation of the significance of each ofthe several aspects of the present invention.

FIGURES 1 to 14 illustrate a turbine meter constituting a practicalembodiment of the principles of the present invention for use inmetering all fluids except of high viscosity, this particular embodimentbeing particularly adapted in certain aspects for use in metering gases.Referring to FIGURES 1, 2 and 3, the turbine meter 20 is provided with aseparable two-part housing comprising a first tubular inlet section 22having an attachment pipe flange 24 welded to its outer end, and acoupling flange 26 welded thereto at its inner end, a second tubularoutlet member 28 of equal diameter to tubular member 22 and coaxiallyaligned therewith and having a pipe attachment flange 30 welded to itsouter end and a flange 32 welded to its inner end and in abutment withthe flange 26 of member 22. As is clearly illustrated in FIGURE 2, theflanges 26 and 32 are piloted together in axial alignment and rigidlyconnected by equiangularly disposed screws 34. Fluid tight relationshipbetween flanges 26 and 32 is maintained by an O-ring type sealingelement 36 retained and compressed in an annular recess in the face offlange 26 abutting flange 32. The internal diameter of tubular members22 and 28 is preferably equal to that of the conduit in which the meter20 is interposed for fluid flow measuring purposes.

A suitably faired two-part core structure, consisting of an upstreamunit 38 and a downstream unit 40, is mounted within the tubular members22 and 28, respectively, in coaxial alignment therewith and houses thefluid metering structure and register drive mechanism. Core structureunits 38 and 40 coact with the inner walls of members 22 and 28 to forma venturi of hollow form (constructed in accordance with the principleshereinafter set forth in detail) between the inlet end of meter 20 atflange 24 and the outlet end thereof at flange 30.

Core unit 38 comprises a hollow body member 42 having an end recess 44receiving a bearing support 46 in axial alignment therewith and fixedthereto by screws 48, a plate 50 rigidly secured at the opposite end ofmember 42 by screws 52 and a nose piece 54 rigidly mounted upon theplate 50 by a stud bolt 56. The exterior surface 58 of the nose piece 54is of suitable diverging crosssection in the direction of flow toconvert the flow of gas or other fluid being metered from thecylindrical stream of the conduit being metered into an annular streamin the annular channel 60 defined between the exterior cylindricalsurface of core member 42 and the interior cylindrical surface ofhousing member 22 constituting the venturi throat. Core unit 38 iscoaxially supported within the tubular member 22 by radially extendingribs 62 which are equiangularly spaced about the common axis of the coreunit 38 and tubular member 22 and which are rigidly connected to coremember 42 by screws 64 and rigidly fixed to tubular member 22 by screws66. Ribs 62 are faired at their opposite ends to minimize the turbulencein the stream resulting therefrom and are of such axial length as toeliminate any tangential component of the velocity of the fluid streamso that as the stream approaches the end of member 22, it hassubstantially pure axial flow.

The downstream core unit 40 is formed by a hollow member 68, theexterior surface 70 of which converges in the direction of fluid flowfrom a cylindrical portion 72 coaxial with and of equal diameter to theexterior surface of the member 42 to a tip 74 and is of suitablecurvature to restore the pattern of fluid flow from the annular channel60 to the cylindrical channel of the downstream pipe with minimumturbulence and minimum head loss. Member 68 is coaxially supportedwithin the tubular member 28 by equiangularly spaced pairs of studs 76and 78 which are threaded into the member 68 and by screws 80 whichextend through the wall of the tubular member 28 and are threaded intothe ends of the studs 76 and 78. A plate 82, apertured at 84, is mountedupon the end of member 68 adjacent the core unit 28 and supports athrust bearing retainer 86.

The meter rotor assembly 88 consists of a shaft 90 formed of magneticmaterial journalled upon the member 46 by spaced radial bearings 92 and94 and magnetically suspended by a predemagnetized permanent horseshoemagnet 96 mounted in the member 46 above the shaft 90, a spoked rotorwheel 98 terminating in equiangularly spaced turbine blades 100 at theperiphery thereof disposed within and extending across the annularchannel 60, and a permanent magnet type magnetic drive coupling drivingelement 102 fixed to the opposite end of shaft 90 exteriorly of thebearing 92. Bearings 92 and 94 are olived ring sapphire radial bearings.Their main function is to define the radial position of the rotor 88.They carry very little load since the weight of the rotor is supportedby the magnetic suspension force of magnet 96 and the rotor is very wellbalanced. The small axial movement of the rotor 88 and shaft 90 (0.010to 0.015 in.) during starting and stopping of the meter makes radialbearings 92 and 94 self cleaning. The resultant magnetic force of magnet96 is of such magnitude as to counterbalance the weight of the rotorassembly 88, its line of action being through the center of gravity ofassembly 88. The total weight of assembly 88 in one practical embodimentof the invention is 0.16 lb. and its moment of inertia is 0.50 1b.-inThe permanent magnet 96 is properly predemagnetized to such an extentthat it will retain its residual magnetization indefinitely after it isinstalled in the turbine assembly. There should be sufficient gap (0.1in. approximately in that practical embodiment) between the magnet 96and shaft 90 so that unavoidable radial play of shaft 90 in bearings 92and 94 does not change the magnetic force appreciably.

The turbine wheel 98 of the rotor 88 is disposed between the adjacentends of core units 38 and 40 at the juncture of flanges 26 and 32 onhousing members 22 and 28 and is readily accessible for servicing byremoval of the tubular member 28 together with the core unit 40 mountedtherein after detachment of the flanges 26 and 32. With the tubularmember 28 and core unit 40 thus removed, the entire rotor assembly canbe removed as a unit by removing screws 48 to detach the bearing support46 from the core member 42. This sub-assemby is shown in FIGURE 7.

As the turbine meter shown in FIGURE 2 is basically designed for gasmeasurement, the structure of the turbine wheel 98 has the form similarto that shown in detail in FIGURES 4 to 12. It comprises a small hub 97fixed to the end of shaft 90, having a plurality (eighteen in thedisclosed embodiment) of spokes 99 projecting therefrom and eachsupporting one of a like plurality of blades 100. The blades 100 are ofhollow construction formed of thin sheet material formed to the contoursillustrated in FIGURES 9 to 12. Blades 100 are straight symmetrical lowdrag air foils with zero overlap (resulting in a solidity 2:1.21). Thechords form an angle of 55.5 with the rotor axis in the illustratedembodiment. If slightly higher starting flow is acceptacle, the profiledair foils may be replaced by straight fiat plates in order to reducecost.

Referring to FIGURE 4, thrust force of the rotor 88 is absorbed by asapphire thrust bearing mounted on plug 104 which is resiliently backedby a compression spring 106 and mounted in the member 86 of the coreunit 40 in axial alignment with the rotor assembly 88. The resilientsupport of this bearing prevents damage thereto during shipment. Thenormal thrust of the rotor 88 is very small, about 0.14 lb. at ratedcapacity of 20,000 ft. 3/ hr. for air at atmospheric pressure in thesaid illustrated practical embodiment.

As is shown in FIGURES 4 and 5, the outer wall of the straight flowannular passage 60 of the turbine meter has a recess 107, properlyproportioned for stability of flow into which the tips of the rotorblades 100 protrude with ample clearance radially and exactly 34 ormore.

Due to its inertia, fluid being metered passes through the straight flowannular passage 60 without deviating into the recess 107. The stabilityof this flow pattern is greatly strengthened by the centrifugal effectof the rigid body rotation of the fluid inside the recess 107 caused bythe rotation of the blades 100. This device, which is denominated hereina turblent seal, eliminates completely the leakage effect of theclearance between the rotor blades 100 and turbine housing 22, 26, 32,and 28 which otherwise is the main cause of the drop of accuracy ofconventional type of turbine meter with increasing flow.

Referring to FIGURES 2 and 13, the magnetic driving element 102 mountedon the left end of turbine rotor shaft 90 is magnetically coupled to amagnetic follower element 108 through a closed and non-magnetic tubularpartition 110 forming a static fluid seal and which is mounted in fluidtight relation with the member 42 by a support plate 112 which is fixedto the member 42 by screws 114 and which is maintained in fluid tightrelation therewith by a compressed O-ring 116 recessed in member 42 andwith tubular partition 110 by a compressed O-ring 118 recessed in plate112. The magnetic follower element 108 drives a pinion 120 which througha suitable gear train, as shown in FIGURES 2 and 3, is coupled to avertically extending shaft 122 which is coaxially aligned with andcoupled to a register drive shaft 124. Register drive shaft 124 (FIGURE3) extends through a fixed tubular housing 126. Housing 126 extendsthrough the annular channel 60 between members 22 and 42, being fixed tomember 42 by an insert plug 128 which, in assembly, becomessubstantially an integral part of member 42. Static fluid tight relationbetween housing 126 and plug 128 is established by an O-ring 130;housing 126 is mounted on member 22 by an insert member 132 welded tomember 22. O-ring 134 forms a static fluid tight seal between housing126 and insert 132.

The shaft 124 is coupled to an input shaft 136 of a conventional dialtype indicator 138 (FIGURES 1 and 3) which is mounted upon the top ofthe meter 20 within an upstanding tubular housing 140 rigidly fixed insubstantial radial relation to the exterior of the tubular member 22.

Referring now to FIGURES 13 and 14, the gear train between pinion 120and shaft 122 is mounted on a pair of supports 144 and 146 which arerigidly connected by screws 148 and which are mounted upon the integralextension of the tubular partition 110 by a bracket 150. Bracket 150 isrigidly connected by screws 152 to the member 144 and is provided with acentral aperture 154 in which is received in a piloting fit thecylindrical portion 156 of the tubular partition 110, the bracket 150being in abutment with a radially extending flange 158 on tubularpartition 110. The fit between aperture 154 and cylindrical portion 156may either be a force fit or the elements may be braised together orotherwise fixed together to form a rigid assembly.

The gear train between pinion 120 and shaft 122 consists of a gear 160journalled on member 144 in constant mesh with pinion 120, a pinion 162rigidly coaxially fixed to the gear 160, a gear 164 journalled on themember 144 in constant mesh with the pinion 162, a pinion 166 rigidlycoaxially fixed to the gear 164, a gear 168 journalled upon a boss 170integal with the member 144 in constant mesh with the pinion 166, a gear172 connected through member 146 by a shaft 174 for unitary coaxialrotation with gear 168, a gear 176 journalled on the plate 144 and 146by a shaft 178 in constant mesh with the gear 172, a worm gear 180 fixedon the shaft 178, and a worm wheel 182 fixed on the shaft 122 and inconstant mesh with the worm gear 180.

Structurally the magnetic drive coupling driving element 102 consists ofa stainless steel yoke 184 coaxially fixed to the turbine rotor shaft 90and a pair of square bar magnets 186 and 188 fixed in recesses 190 and192 on the arms of the yoke 184 as by soft soldering. The longitudinalcentral axes of the square bar magnets 186 and 188 are equally spacedfrom the axis of the shaft 90 and parallel thereto and are disposed inequiangularly arranged surrounding relation to the tubular partition110.

The follower magnet assembly is disposed within the closed and tubularwell 194 of the tubular partition 110 and is mounted therein for coaxialrotation by a shaft 196 which is journalled in spaced bearings 198 and200 which are supported by mating tubular bearing retainer members 204and 206 respectively. Members 204 and 206 are maintained in coaxialalignment by the piloting engagement of the cylindrical surface 208 onmember 206 with the cylindrical recess 210 in member 204 and arereceived in a piloting fit with the internal cylindrical wall of thetubular partition 110. Follower member 108 comprises a cylindricalplastic magnet support 212 having diametrically opposed semi-cylindricalrecesses 214 and 216 cut in the periphery thereof to receive cylindricalfollower magnets 218 and 220 respectively. Magnets 218 and 220 arepreferably substantially coextensive in length with the driving magnets186 and 188 are maintained in alignment therewith along the common axisof shaft 90 and 196. The plastic magnet support 212 is fixed to theshaft 196 for rotation therewith by a pair of support pins 222 thecoplanar axes of which are parallel to the axis of shaft 196 and offsetfrom the recesses 214 and 216 and which project through apertures in theplastic magnet support 212 and which are supported at their free end bya flange 224 which is rigidly fixed coaxially to the shaft 196 to theright of the bearing 200.

As is explained fully in our said copending application Serial Number634,662, the relation between the driving magnets 186 and 188 and thefollower magnets 218 and 220 is such that, as the shaft 90 is rotated inresponse to fiuid flow through the turbine blades 100 of the rotorassembly 88, the follower assembly 108 will be caused to rotate eitherby attraction of the follower magnets 218 and 220 to the driving magnets186 and 188 or by repulsion of the follower magnets 218 and 220 from thedriving magnets 186 and 188. The repulsion type drive coupling, becauseof its substantially lower backload on the turbine rotor 98, ispresently considered essential for accuracy in metering low densityfluids such as gases. In case of large size turbine meter in meteringliquids, some backload on the turbine rotor can be tolerated withoutappreciable effect on the meter accuracy. The attraction type drivecoupling is preferred because of its higher transmission torque, higheracceleration and higher pickup speed than the repulsion type of samesize. Rotation of the follower 108 imparts rotation to the shaft 196 andthe pinion 120 which is fixed to the end thereof exteriorly of thebearing 198 to impart rotation to the register drive shaft 122 throughthe gear train illustrated in FIGURES 13 and 14 and previouslydescribed.

From the foregoing description, it is apparent from FIGURES 2 and 3,that the plate 50, seal 51, member 42, plate 112, seals 116 and 118 andtubular partition 110 define a sealed chamber 230 which is isolated fromthe fluid flowing through the channel 60 by the tubular housing 126which is provided with seals 130 and 134 the rotary motion of thefollower 108 is transmitted to the register mechanism 138 exteriorly ofthe meter housing members 22 and 23 without the use of any dynamic fluidseals such as stuffing boxes and thus provide a fluid tight registerassembly with very small mechanical friction. If further detailedinformation is considered to be necessary as to the detailedconstruction of the magnetic drive coupling, reference is hereby made tothe disclossure of our said copending application Serial Number FIGURE15 illustrates a modified version of the turbine meter of FIGURES 1 to14. The FIGURE 15 embodiment is particularly adapted for meteringliquids and, in the actual physical embodiment, is substantially largerthan the embodiment of FIGURES 1 to 14. Structurally the meters areidentical with the exception of the rotor structure and mounting. Themeter comprises coaxial tubular housing sections 300 and 302 fixedtogether by bolts 304 and maintained in fluid tight relation by acompressed O-ring 306, coaxial equal diameter core sections 308 and 310coaxially mounted in housing sections 300 and 302 respectively to definean annular channel 312 forming the throat of a venturi of hollow form,and a turbine rotor 314 interposed between the opposed ends of coresections 308 and 310.

The turbine rotor 314 comprises a central hub 316 fixed to a shaft 318which is journalled at its opposite ends by opposed ball thrust typeanti-friction bearings 320 and 322 carried coaxially by core sections308 and 310 respectively, an annular rim 324 supported from hub 316 by aplurality of spokes 326 arranged substantially in the same manner as thewire spokes of a bicycle wheel, and a plurality of equiangularlydisposed blades 328 mounted on the exterior of the rim 324 to extendtransversely across the passage 312, the tips thereof projecting into anannular recess 330 forming a turbulent seal as in the first embodiment.

The blades 328, as is clearly shown in FIGURES 16 to 18 are solid,symmetrical, but twisted airfoil blades inserted in the ring. Each blade328 is so twisted that it has the same angle of attack for uniform axialvelocity distribution of inlet flow throughout the entire length of theblade from root to tip. The blade angle is 55.5 at blade tip and isreduced to 415 at blade root, both measured from the axial direction.The length of the chord of the blades are such that zero overlap betweenblades is maintained throughout the entire length of the bladesresulting in a solidity a: 1.2 at blade tip and :15 at blade root.

In the meter of FIGURE 15, the register is located downstream of theturbine rotor 314, being driven from a shaft 332 which is drive coupledto the turbine rotor shaft 318 as shown. The structure of the registerand its coupling through a magnetic drive coupling to shaft 332 is thesame as in the first embodiment. No magnetic suspension of the turbinerotor 314 or shaft 332 of turbine meter of large size is necessary inmetering liquids and the magnetic drive coupling to the register may beof the attraction type in metering liquids.

ANALYSIS OF THE TURBINE METER IN FLUIDS OF LOW AND MEDIUM VISCOSITIES A.Starting condition (FIGURES 19 to 21) By means of flow straighteners andproper design of the turbine housing and approaching hub, the inletvelocity 11 to the turbine blade can be assumed to be purely axial anduniformly distributed across the entire annular flow passage.

Consider first the instant just before the turbine starts to rotate. Thedriving torqueT exerted on the blades by the fluid is just in balancewith the total resisting torque T with turbine standing still. FIGURE 21shows the velocity diagrams at this instant.

The driving torque dT on the blade elements within the annular stream drbetween Sections 1 and 2 of the blades at radius r from the axis ofrotation (FIGURES 19 and 20) is found from the angular-momentum law tobe a=(p Q) where dQ rate of flow through the stream tube dr,

=mass density of the fluid r =tangential component of the absoluteoutlet velocity v at distance r from axis of rotation.

It can be shown that the element dr of the blades will behave as thoughit had a constant inlet velocity over its radial length equal to that atthe mean radius r where where Q =rate of flow just before the turbinestarts to rotate,

henceforth called starting flow.

m tangential component of absolute outlet velocity 11 at mean radius rAssume the flow through the blades is incompressible or strictlyuncompressed. This can be justified here even for gases because thepressure drop across the properly designed blades is extremely low incomparison with the line pressure Then by continuity and by thecondition that the diameters of hub and housing are uniform betweenSections 1 and 2:

the effective flow area of annular cross section. turbine meter of whichwhere For a "0 is not far from unity, Aaz21rr L for first approximationwhere L: (r r the effective blade length.

Thus m,, tan ma =g (4) where m, is the fluid outlet angle at mean radiusr tan m measured from the axial direction, substitute (4) into (3) 5 KOr, expressing in terms of inlet'flow velocity 1 in the annular crosssection,

starting condition K depends largely upon the particular design andarrangement of the rotor and the relative clearance between the rotorand its adjacent stationary parts. The accurate determination of K canonly be obtained by actual test.

g dimensionless coefficient determining T henceforth called turbentcoefficient of the turbine meter at the starting condition. K dependslargely upon the particular shape of the blades, blade angles andsolidity ratio of the blade system. The accurate determination of'K canonly be obtained by actual test.

From Equations 5, 6 and 7, the starting flow Q can be solved and isgiven by T =7' A tan mu Equations 5 and 5a indicate that the drivingtorque available for a given turbine meter is directly proportional tothe density p of the-fluid and proportional to the square of the flowrate (or inlet flow velocity). For a given inlet flow velocity of agiven fluid, T increases approximately with the third power of the meanradius of the meter and increases with the increase of the fluid outletangle a measured from the axial direction. Both experiment and analysisreveal that the blades of a high accuracy turbine meter should besufficiently close so that the deviation betweenthe actual outletdirection u of the fluid flow and the blade outlet angle {3 isnegligibly small, i.e., fi /3 Then T tan m z og (5b) Atstartingcondition, the drivingtorque equals the total resisting torque T '=T,.The total resisting torque T consists of mechanical friction T and fluidfriction T The mechanical friction T which contains mainly bearingfriction and register load is of Coulomb nature, is independent of flowrateQ. The fluid friction T which consists mainly of the blade entranceloss, blade profile drag loss and the blade'exit loss, depends upon theflow rate Q, the density p, the viscosity 1. of the fluid, and thegeometric arrangement of the blade system. Because of the complicatednature of the flow pattern through the blade system, the determinationof individual items of fluid friction is difficult with the presentknowledge of fluid mechanics. However, the fluid friction T; can beconsidered to consist of the following: (1) resisting torque T, due toviscous friction which is controlled by viscosity forces and is linearlyproportional to flow velocity, (2) resisting torque T due to turbulentfriction which is controlled by inertia forces and is proportional tothe square of the flow velocity. Then, the total resisting torque can beexpressed as K =dimensionless coefficient determine T,- henceforthcalled viscous coefficient of the turbine meter at For all fluids (suchas air, gases, water, gasoline, thin fuel oil, etc.) except of highviscosity and for turbine meters specially designed to attain minimumvalue of the viscous coeflicient K the viscous friction T, is usuallyconsiderably smaller than either the turbulent friction T, or themechanical friction T at starting condition. Equation 8 then becomes s zT 1, 2W1] [tan m,B Both theoretical analysis and actual test resultsindicate that there is a definite relation between the starting flow Qand the minimum flow of the operating flow range Q For a properlydesigned turbine meter forfluids' of low viscosity depending upon theaccuracy requirement of the turbine meter. It becomes thus evident thatlow value of starting flow Q is one of the necessary conditions for ahigh accuracy turbine meter with large operating flow range or largeflow ratio. The following conclusions are derived from the study ofEquations 8 and 9.

(l) The mechanical friction T should be made as low as practical.

(2) The blades should be reasonably short for given diameter of theturbine meter to obtain low values of B. Synchronous conditionSynchronous here is used to indicate the condition when the turbinemeter is in steady rotation. Again, from the angular-momentum theorem,the driving torque T available at synchronous condition is 1 1 Fromvelocity diagram as shown in FIGURES 22 and 23 m,, =i tan m r w where wis the angular velocity of the turbine rotor.

Therefore T tan m ]pQ n Q At synchronous condition where C=dimensionless coefficient determining viscous friction T henceforthcalled viscous coefficient of the turbine meter at synchronouscondition. C depends largely upon the design of the blades as well asthe entire rotor assembly, the relative clearance between the rotorassembly and its adjacent stationary parts. The accurate determinationof C can only be obtained by actual test.

C dimensionless coefficient determining turbulent friction T henceforthcalled turbulent coefficient of the turbine meter at synchronouscondition. C depends largely upon the shape the blade angles andsolidity ratio of the blade system, the design of the rotor spokes (ordisc) and other parts of the rotor assembly. The accurate determinationof C can only be obtained by actual test.

It is noted that while at synchronous condition the mechanical frictionT is essentially the same as in the case of starting condition, thecoeflicients C and C of both the viscous friction T and turbulentfriction T are somewhat difrerent from K, and K (Equation 7) for thestarting condition. This is due to the following main reasons:

(a) Since the rotor assembly is no longer standing still, there areadditional fluid frictions besides blade losses due to the rotation ofthe rotor spokes (or disc) rotor hub and other parts of the rotorassembly. Strictly speaking, these fluid frictions depend upon therotating speed of the rotor rather than flow rate Q. However, within theoperating range of the turbine meter wczQ. Equation 11 can therefore bejustified. The presence of these additional fluid frictions tends toraise the values of C and C over K and K respectively.

(b) The angle of attack t =(B a of the blade system at synchronous speedis much smaller than the angle of attack t =fi at starting condition.This decrease in blade losses tends to reduce values of C and Cconsiderably below K, and K respectively.

Equating Equations 10 and 11 and solving for AH V Or, as expressed indimensionless quantities:

m ub Q/ a V1 where m, =r w=blade velocity at means radius r of theturbine meter.

=Reynolds member of the annular flow pass-agea direct measure of theratio of turbulent friction to viscous friction of the flow.

Equation 12 indicates that the actual speed of the turbine meter perunit flow rate 1 a 7 mils. zzZ

less the slip of the rotor due to the following three componentlosses:(a) slip due to the turbulent friction (b) slip due to theviscous friction i591 m p Q and (c) slip due to the mechanical frictionIt is noted that the slip due to turbulent friction depends upon theturbulent coeflicient C and is independent of the flow rate Q. The slipdue to viscous friction is inversely proportional to Q and thus itseffect on meter accuracy decreases as flow rate Q increases. The slipdue to mechanical friction is inversely proportional to the square ofthe flow rate. It, therefore, has a pronounced effect on the turbinemeter accuracy at low flows and becomes relatively unimportant at highflows.

Except for fluids of high viscosity, the flow in a turbine meter ofreasonable size within its operating flow range will be turbulent innearly all practical applications. With the turbine meter properlydesigned for the low value of the viscous coefiicient C the viscousfriction T =CmQ is usually small in comparison with turbulent frictionwithin the operating flow range.

An ideal turbine meter for direct and accurate measure ment of fluidflow requires that the speed of the turbine meter per unit flow rate (orsimilarly, the number of revolutions of the turbine meter per unitvolume of the fluid passed) remains constant throughout the entireoperating flow range. An

actual turbine meter will approach the ideal if the right side of theEquation 13 B B m flw d M791} is a constant. This defines therequirements for the linear relationship between the turbine speed andthe rate of flow which a turbine meter of high accuracy must meetthroughout its entire operating flow range when dealing with all fluidsincluding those of high viscosity.

(1) The fluid outlet angle a should be constant. This can beaccomplished by using sufiiciently close-spaced blading so that thefluid outlet angle a approaches the blade outlet angle ,8 withnegligible deviation, i.e., u =fl =constant.

(2) The mechanical friction T must be made small so that the slip of therotor due to T should be negligible even at Q (minimum flow of theoperating flow range). For a turbine meter measuring fluids of lowdensity such gases at low pressure, the mechanical friction T isespecially harmful and must be reduced to a bare minimum since the slipis inversely proportional to the fluid density p [Equation 13].

(3) The turbulent coefficient C, of the turbine meter should remain aconstant for all flow rates within the entire operating flow range.Since C does vary somewhat with flow rate, the value of C, should beminimized. These two requirements of C can be approached by usingproperly designed low drag airfoil blades with optimum blade angles,twist and solidity (blade length/blade spacing) together with properlydesigned annular flow passage both upstream and immediately downstreamof the rotating blades.

(4) The viscous coeflicient C should be kept as low as practical. Thissuggests that (i) close running clearances should be avoided wheneverpossible, (ii) surface area of the rotor assembly subjected to viscousfriction be kept to a bare minimum.

C. Minimum flow of the operating flow range-Q 1 Qmin z Ye-QB If theallowable error e=0.5

' Qmin- 10 Qs I f E=0.2

Qmin Qs D. Angle of incidence of the blade system and the angle of fluiddeflection For a properly designed turbine meter working within itsrange, the angle of incidence of the blade system and the angle of fluiddeflection when passing through the blades (angles L and 5 respectively,FIGURES 22 and 23) can be readily estimated as follows:

Experimental results and analysis indicate that the total slip of a welldesigned turbine meter (fi ot working in its operating range is wellwithin 7%,

M2 or v tan m 0.07 tan m For the sake of simple construction and lowcost, it is very desirable to use symmetrical blades if they givesatisfactory performance (to be discussed in detail later). For asymmetrical blade system =tan m a From Equation (15) tan m,, (tan m-0.07 tan m )=0.93 tan m (16) For the desirable range of blade angle 40fi 60 (to be discussed in detail later), Equation 16 gives:

B2 n1) fi1 a1) for symmetric blade system and is the angle of incidenceof the blade system at the mean radius r (FIGURE 23). Therefore m=arctan or tan m From Equation 15 0.07 tan 771,5

tan m (18) For desirable range of blade angle 40 m 60. Equation 18 givesSince the fluid possesses very low tangential velocity when leaving theblade system as indicated by the above equation, no pressure recoveryshould be attempted.

E. Head loss of the turbine meter The total head loss across a turbinemeter, H, can be separated into two parts: (i) loss across the movingblades. Let it be designated as the blade loss H-,,, and (ii) all otherlosses across the meter, mainly by the loss due to venturi. Let it bedesignated as the venturi loss H,.

The blade loss could be further separated as (a) loss to overcomemechanical friction, (b) loss due to profile drag on the blades, (c)loss due to annular drag corresponding to friction of walls and (d)secondary flow losses such as loss due to trailing vortices, etc.However, within the operating flow range of the turbine meter, the bladeloss can be treated as a whole by the use of an overall loss coeflicientC design and operating conditions, especially the angle of attack.Actual value of C can be found by test.

But from Figures 22 and 23,

vaZ 1 cos m A cos m vR z l R2 Then v v 1/2 P a p where v zflllidvelocity in the annular cross section 1 or 2.

u =fluid velocity in the pipeline before entering or after leaving themeter.

C,,::venturi loss coefficient depending upon the design of the flowpassage through the meter, the area ratio, and Reynolds number. It canbe determined by actual test.

But

where A is the cross-sectional area of the pipe The total head loss ofthe turbine meter is thus equal to From the above equation, it is notedthat (1) The head loss of the meter is directly proportional to thedensity of fluid passing through the meter since Hap. For gas at a giventemperature, pap where p is essentially the line pressure, the absolutehead loss of a turbine gas meter is directly proportional to the linepressure.

(2) The head loss of the meter is proportional to the square of the flowrate since HOLQZ. Therefore, the maximum head loss of the meter occursat maximum flow rate (3) Low head loss requires large annular flow areaA of the meter, less slanted blades (i.e., small blade angle ,8 measuredfrom the axial direction) and a venturi flow path with low flow loss butstill economic dimensions.

F. Transient response of the turbine meter The transient response of theturbine meter is best described by the time constant of the rotor whensubjected to a step change in fluid velocity. That is, if aninstantaneous increase occurs in the flow rate, say from Q to Q therotor will accelerate from a speed m corresponding to the original flowrate Q to a speed (0 corresponding to the new flow rate Q The timerequired to accelerate the rotor to its new speed (or some fraction ofits new speed) is a measure of the time constant of the rotor.

Assume both Q and Q are within the operating flow range of the meter.Let in be the instantaneous speed of the rotor at any instant t duringthe period of acceleration of the rotor. At the new constant flow rate Qthe driving torque and the resisting torque are given by Equations and11 respectively The last approximation can be justified for a turbinemeter working within its operating range and for fluids not of highviscosity. Since w w therefore T T,. By Newtons 2nd law of motion whereI is the moment of inertia of the rotor assembly about the axis of therotor. From the last three equations together with the Equation 12 whichgives the approximate relation Tm t, Tnzi/i. mi

it can be readily shown that t do:

di=f Ji) wi m PQ2( tfie) (2%)] Or, the above equation can be expressedin another form to give the rotor speed to as a function of time t:

where e is the base of natural logarithms. Equation 24a is plotted inFIGURE 24. It is seen that the rotor speed to is an exponential functionof time and its time constant 7' is (l/I pQ which is the time requiredfor the rotor to attain of the imposed velocity increment (LUZ-(.01).This time required is directly proportional to the moment of inertia Iand inversely proportional to the square of mean radius r fluid densityp and the flow rate Q Let us consider the case of a turbine meter with atime constant r=I/r Q used to measure a highly fluctuating flow having awave form close to a square wave as shown by the solid curve in FIGURE26. The average flow rate is the amplitude of the wave, a; and theperiod of the wave, v- From the above analysis, the turbine meter willrespond according to an exponential curve as indicated by the dottedcurve in FIGURE 26. It can be shown analytically that the turbine meterwill overrun and the transient error in percentage is given by thefollowing equation:

a i (a noted that the transient error of a turbine meter depends uponthe nature of the fluctuating flow itself as well as the meter. For agiven turbine meter, the transient error increases with the percentagefluctuation of the flow. For a given fluctuating flow, the transient andfrequency error is approximately proportional to the time constant 7 ofthe meter. A turbine meter for accurate measuremen? of p ating flow musttherefore have a very low time 17 constant 1-=(I/r Q) in order that thetransient error Will be small even for a fluctuating flow of highfrequency and large amplitude. The following conclusion can then be madebased upon the above analysis:

(1) The moment of inertia of the rotor assembly should be made as low aspermitted by strength, rigidity and functional relations of the variousparts of the rotor assembly.

(2) With a given moment of inertia of the rotor assembly, the meanradius r of the rotor should be made as large as practical withoutviolating other requirements such as low head loss, moderate rotorspeed, etc.

(3) The transient response of the turbine meter is considerably morecritical in gases than in liquids since the time constant is inverselyproportional to the fluid density.

IMPORTANT STRUCTURAL CHARACTERISTICS OF THE TURBINE METER OF THE PRESENTINVENTION Based on the preceding theory of the turbine metersupplemented with actual experience and test results of several turbinemeters designed according to the theory (and tested in air, natural gas,water, gasoline, stoddards solvent, thin oil and thick oil), someimportant design criteria and the resulting structural features of theturbine meter as disclosed in this application will be discussed brieflyas follows:

(1) Turbulent seal In the preceding analysis, a uniform velocitydistribution across the annular cross-section is assumed and the effectof induced drag due to finite blade length is taken as being negligiblysmall. The conventional means of satisfying this requrement is to keepthe blade tip clearance less than 2% of the blade length. This smallclearance not only demands close manufacturing tolerances, but alsopresents a source of potential trouble from entrained particles in thefluid. However, the abovementioned assumptions can also be satisfied bythe use of a novel device referred to as a turbulent seal.

The straight flow passage 60 (FIGURES 4 and 5) of the turbine meter hasa properly proportioned recess 107 (for stability of flow) into whichthe rotor blades 100 protrude, or are at least flush with the recess(i.e., blade tip diameter D D the turbine housing diameter) with ampleclearances as shown in FIGURE 5. The axial length of recess 107 ispreferably substantially equal to an even whole number multiple of theradial depth thereof.

Due to its inertia, the fluid passes through the straight flow passage60' without deviating into the recess 107. The stability of this flowpattern is greatly strengthened by the centrifugal effect of therotation of the fluid inside the recess 107 induced by the rotation ofthe blades 100-. This novel device, referred to as a turbulent seal,eliminates completely the leakage effect of clearance between the tipsof the rotor blades 100 and turbine housing 22, 26, 32 and 28, for flowseven below Q Its unusually large physical clearance eliminates anypotential trouble due to entrained particles in the flow as well aseliminating close manufacturing tolerances thereby resulting in lowercost. The breaking or retarding torque induced in the turbulent seal,and exerted on the turbine rotor bears the same functional relation toflow as the driving torque [i.e., it just increases the value of C, inEquation 13], resulting in a lowering of the registration curve of themeter by a constant amount throughout the entire operating flow rangewithout changing its nature. Since this amount of lowering of theregistration curve is the same for all fluids, it can be once and forall corrected by direct calibration of the meter register. Endurancetests also indicate that the recess is kept clean by the sweeping actionof the turbine blades.

From the discussions of Equations 9, 14, and 13, it is concluded thatthe performance of the turbine meter at the lower end of its operatingflow range is governed primarily by the magnitude of the mechanicalfriction T present in the meter. This effect of mechanical friction isespecially critical for turbine meters used for measurement of fluids oflow density such as gases, since the slip of the rotor to overcome agiven mechanical friction is inversely proportional to the fluid density[Equation 12]. For a turbine gas meter, the bearing friction due to theweight of the rotor assembly constitutes an important part of themechanical friction T and must be kept to a minimum consistent with themechanical strength and rigidity of the rotor assembly and goodmanufacturing practice. However, the effect on mechanical friction ofthe weight of the rotor assembly can be almost completely eliminated bya very simple, but effective device referred to as the magneticsuspension of the turbine rotor assembly.

The weight of the rotor assembly is practically balanced by the magneticattractive force exerted on the rotor shaft by a suitable permanentmagnet properly positioned (such as a horseshoe-shaped permanent magnet96 in FIGURE 2). The permanent magnet is initially slightly demagnetizedso that its residual magnetization will remain constant indefinitelyafter installation in the meter. The position of the magnet is such thatthe resultant magnetic attraction has approximately the same line ofaction as the resultant gravity force of the rotor assembly. Thereshould be sufficient gap between the magnet 96 and the rotor shaft sothat anyallowable radial play of the rotor shaft 90 within its radialbearings 92 and 94 does not change appreciably the magnitude of themagnetic force. Therefore, the main function of the radial bearings isto define the radial position of the rotor. Since the rotor isstatically and dynamically balanced and the weight of the rotor assemblyis taken by the magnetic suspension, these bearings 92 and 94 carry verylittle load, resulting in long bearing life and very low bearingfriction. This low bearing friction gives much better meter performance(especially at low flow rates) and a much wider flow range.

(3) Magnetic drive to the sealed register One of the most importantproblems that existed in direct registering flow meter was the provisionof a suitable coupling between the metering element and anexternalregister, while maintaining a fluid tight seal. Conventional dynamicseals such as a stuifing box or an ordinary magnetie coupling might worksatisfactorily for positive displacement type flow meters. However,these seals cannot be tolerated by high accuracy turbine meters mainlybecause of their excessive mechanical friction imposed on the rotorassembly. A new type of magnetic drive referred to as the doublerepulsion type (one form of this type is shown in FIGURE 13) has beendeveloped and works very satisfactorily with turbine gas meters such asthe one shown in FIGURE 2. It introduces practically no mechanicalfriction, has very low moment of inertia, high pick-up speed andreasonably high transmission torque. In the case of the turbine liquidmeter (FIGURE 15) which can tolerate some small mechanical friction, adouble attraction type magnetic drive is most suitable because of itshigher transmission torque and higher pick-up speed. The detaileddescription of these new types of magnetic drives is disclosed in oursaid copending patent application Serial Number 634,662.

(4) Diameter ratio Except in some special cases, the diameter of theturbine housing is made equal to the diameter of the pipe into which theturbine meter is inserted for flow measurement. This design has thefollowing advantages:

(i) Permits in-the-line installation,

(ii) Results in minimum change in flow direction,

(iii) Allows compact design.

The ratio of the core diameter to the turbine housing diameter DL/Do(FIGURE 19 or 20) is directly related to the head loss, starting flow,blade design and rotor speed. Low head loss requires large flow area,therefore low DL/Do ratio [Equation 22] Whereas low starting flowdemands high inlet velocity, therefore large DL/Do ratio [Equation 9].If straight blades are to be used for the sake of low manufacturing costas in FIGURE 4, the DL/DO ratio should not be less than 0.75 in order tomaintain reasonably good blade efficiency throughout the entire lengthof the blade. For a given flow rate and a given blade angle, the rotorspeed is directly determined by the DL/DQ ratio. The value of the DL/Doratio should be such that it gives an optimum operating range of rotorspeeds with regard to sensitivity, resolution and life of the turbinemeter. Therefore, the proper value of the DL/Do ratio of the turbinemeter must be a compromise of the requirements discussed above.

Analysis and experimental results indicate that the optimum values ofthe diameter ratio of the turbine meter are For values of straightblades can be used with little loss in overall blade efliciency (to bediscussed more in detail later).

() Core design The design of the core 38, 40, of a turbine meter (FIG-URE 2) is based on the following three requirements:

(i) Providing a flow passage which gives as close to uniformlydistributed purely axial inlet velocity as possible.

(ii) Low venturi loss.

(iii) Minimum length consistent with (i) and (ii).

The generally desirable shape of the core is shown by the one in FIGURE2. Starting from the upstream end, the core has a comparatively bluntnose followed by a long straight portion leading to the rotor blades100. Downstream from the blades 100, it has a short straight portionfollowed by a tail piece, which tapers first gradually and then moresharply. The profile of the core is such that the rate of change of boththe magnitude and the direction of the flow velocity is continuous andmoderate. The venturi loss coefficient C defined in Equation 21 for thecore shown in FIGURE 2 is found to be less than 0.5 by actual test.

(6) Blade cross-section Following the discussion of Equations 9 and 13,it is evident that the airfoil blades will give better performance thanthe flat plate blades, particularly at low flow rates. The former has alarger stalling angle, higher lift and lower drag for a given angle ofattack, resulting in a larger driving torque for a given slip of therotor and a smaller value of the turbulent coefiicient K and thus alower value of starting flow [Equation 9]. Also, within a small range ofangle of attack, both the absolute magnitude and the amount of variationof the drag coeflicient [which determines primarily the value ofturbulent coeflicient C in Equation 13] are appreciably smaller whenairfoil sections are used rather than fiat plates, resulting in a betterlinear relation between turbine speed and flow rate over a wider rangeof flow. Another advantage of airfoil sections lies in the fact thatthey permit the desired mechanical strength and rigidity with a minimumsacrifice of blade efficiency. However, for applications where extremelyhigh accuracy and wide flow range are not needed and where low cost isessential, flat plate blades will prove to be satisfactory since atmoderate and high flow rates, the angle of attack is usually very smalland essentially constant [Equation 17].

(7) Blade curvature The blade curvature can be expressed as 5 8 thedifference in blade outlet and inlet angles (FIGURE 21). The angles aretaken from the mean camber line. Theory and actual test results indicatethat the angle of attack for symmetrical blades is less than 2 Withinthe entire operating flow range (Equation 17). Therefore, no bladecurvature is necessary, i.e.,

Besides, symmetric blades are very desirable from the point of view ofmanufacturing and cost. Moreover, improper blade curvature will impairrather than improve the meter performance.

(8) Blade thickness (9) Blade angle For given flow condition, there isan optimum blade setting to give maximum blade efliciency. However, fora turbine meter with symmetrical airfoil blades working within itsoperating flow range, the efiiciency remains good within :10" from itsoptimum blade setting. However, high driving torque requires large bladeangle [Equations 5 and 10] whereas low head loss demands low blade angle[Equation 22]. The desirable range of blade angle 6:5 :5 measured fromthe axial direction is therefore a compromise among the above-mentionedfactors together with the desirable value of the maximum rotor speed andis found experimentally as follows:

The blade angle should be slightly higher for fluids of low density,such as gases, than for fluids of high density, such as liquids.

(10) Solidity It has been emphatically mentioned in the previousanalysis [Discussion under Equations 5a and 13] that the blades of ahigh accuracy turbine meter should be sufliciently close so that thedeviation between the fluid outlet angle a and the blade outlet angle 5is negligibly small and thus a -fi =constant throughout the entireoperating range. Closely spaced blading requires high solidity the ratioof blade chord to blade spacing (FIGURE 21). However, high soliditymeans large total blade area, resulting in high blade profile friction.Therefore, the proper value of solidity should be low enough to insurelow blade friction loss but high enough that the fluid is closely guidedby the blading through an angle practically identical with that of theblading itself. Fortunately, the actual deflection of the fluid causedby the blading 21 is very small [angle 6 6.9 Equation (19)] and onlymoderate value of solidity is needed to obtain the condition az sg.

Experimental results indicate that the following range of solidityproved to be desirable:

The solidity should be slightly higher for compressible fluids, such asgases, than for incompressible fluids, such as liquids.

At .any radius r of a rotor with Z blades, the blade spacing or pitch isThe corresponding value of solidity is thus at mean radius r the chordlength of the blade must increase linearly with radius r so thatHowever, for properly twisted blades to be discussed later, thewbladeangle increases withincrease of radius. A lower value of solidity of ablade system with larger blade angle has the same efiect in guiding theHow as a blade system with high solidity, but smaller blade angle.Therefore, for twisted blades, the solidity is preferred to decreaseslightly at uniform rate from the blade root, say, 6:1.5, to blade tip,say, 6:12, to obtain minimum blade friction. However, the chord lengthof the blade of a turbine meter should always be largest at tip andsmallest at root, just to the contrary of the proper blade form of powerturbines. The smaller chord at blade tip- .and larger chord at bladeroot of blades of power turbines is determined on the basis of stressstandpoint.

'( 11) Number of blades For a given value of solidity, test results showhigher blade etficiency the fewer the blades. 0n the other hand, moreblades result in a more uniform distribution in velocity, pressure andtorque application. Also, for a given solidity, large number of bladesresults in a rotor with shorter axial length, less weight and smallermoment of inertia. Therefore, the optimum value of the number of rotorblades is a compromise of the above discussed factors.

Experiment tests indicate that the desirable range of number of blades Zis 12Z24 31 Thenumber of blades should be slightly larger forcompressible'fiuids, such as gases, than for incompressiblefluids, suchas liquids.

(12) Blade twist (see Figures 15 to 18) The blade is-first designed atmean radius r of the rotor. Based on the assumption that the inletvelocity to the blade L9, approaches a uniform distribution across thecross section. (1) FIGURE 19, the blades are best to be so twisted atother radii that the same angle of attack along the entire length of theblades is maintained. Thismeans that the designed condition of maximumbladeefliciency (Lift/Drag ratio), minimum magnitude and. minimumpossible variation of turbulent coefiicient [C 22 Equation 13] ismaintained along the entire length of the blades resulting in maximumoverall driving torque per unit slip of the rotor, minimum overall fluidfriction and best possible linear relation between the rotor speed andAt any radius r When the blade is so twisted that the angle of attack isthe same along the entire blade length and equal to ma, Equation 3 2abecomes The amount of blade twist at any radius r with respect to theblade angle at mean radium r is thus equal to and the total angle ofblade twist from the blade root to blade tip is given by It is notedfrom Equation 33 that the blade angle increases with the radius r,minimum at blade root and maximum .at blade tip. However, within theabove-men-- tioned desirable range of the diameter ratio of the turbinemeter [Equation 26], the maximum amount of blade twist referring to thedesigned value of blade angle at mean radius is less than :L8. It hasbeen discussed previously under the heading of Blade Angle that theblade angle is not critical and the blade elficiency remains good within:10 from its optimum blade setting. Therefore, the slight variation inblade angle as a result of twisting blade according to the requirementof the same angle of attack along the entire length of the bladescreates no significant objection For a turbine meter with diameter ratiountwisted blades will only cause a variation of angle of attack lessthan 14 from blade root to blade tip resulting in only slight effect onmeter performance especially with airfoil blades. Therefore, for turbinemeters where extreme high accuracy is not required but low cost isessential, especially for small size of meters, straight untwistedblades will prove to be satisfactory in most cases (see FIGURES'IO to12).

FIGURE 15 shows one of the desired forms of the turbine rotor with itsblading in compliance with the specifications given above for thoseturbine meters where extremely high accuracy is essential, while weightand moment of inertia of the rotor and the manufacturing cost are notcritical such as in the case turbine liquid meter of medium or largesize. 0n the other hand, when the weight and the moment of inertia ofthe rotor, as well as the manufacturing cost are critical while theaccuracy requirement is only moderate (say within i0.5% over a flowrange of 10), such as in the case of turbine gas meter, the form ofturbine rotor shown in FIGURES 1 to 12 is more desirable. Straightblades are satisfactory in this case when axial in direction.

From the foregoing analysis, the following important conclusion on theturbine meter designed according to the criteria listed above has beenestablished.

It the mechanical friction T is made small enough that the slip of thertor due ot T becomes insignificant at minimum flow of the operatingflow range in fluids of not high viscosity, Equation 13 is then reducedto When the turbine meter is so designed that the turbulent coefficientC remain a constant; the accuracy curve becomes a single flat curvewithin its operating range. The meter will have the same calibrationconstant for all fluids having different densities and viscosities aslong as the mechanical friction and the viscous drag being small enoughthat the rotor slips due to them are insignificant.

With the turbine operating as a flow measuring device, it will handlelarge volume with low differential pressure. Analysis reveals that theaxial flow type turbine is more suitable than the radial flow or mixedflow type in this particular application. In view of the aboveconsidera- *tion, only an axial flow type turbine meter will be analyzedin detail although the analysis can be extended to other types withoutmuch modification.

The less the flow is disturbed, the lower the flow loss will be, and themore accurate the turbine meter can be made. The direction of the inletflow is thus preferred to be purely axial in the axial flow type turbinemeter since the flow reaching the turbine meter is substantially Properstraightening vanes are needed ahead of the turbine rotor to assureaxial flow for accurate measurement if the turbine meter is to be placedimediately behind a double elbow or other similar arrangement whichcauses a pre-rotation of considerable magnitude.

The invention may be embodied in other specific forms without departingfrom the spirit or essential characteristics thereof. The presentembodiments are therefore to be considered in all respects asillustrative and not restrictive, the scope of the invention beingindicated by the appended claims rather than by the foregoingdescription, and all changes which come within the meaning and range ofequivalency of the claims are therefore intended to be embraced therein.

We claim:

1. In a fluid flow meter, a separable two-part tubular housing havingaxially opposed abutting surfaces and oppositely facing ends providedwith means adapted to establish a connection to a fluid pipeline, a pairof axially spaced apart, aligned cores coaxially mounted in said housingand defining with the inner wall of said housing a longitudinal fluidflow channel of annular cross section, at least the upstream one of saidcores being faired for gradually transposing the cross-sectionalconfiguration of the oncoming fluid stream, means independently fixingsaid cores to respective ones of the housing parts, a rotatable,peripherally bladed metering rotor disposed axially between said coresand having its blades in the path of fluid flowing through said channelto be driven by fluid flow therethrongh, the downstream one of saidcores cooperating with said housing to extend said channel apredetermined axial distance downstream of said rotor, said housingparts abutting each other along an interface contained in a planepassing radially through said rotor, a support detachably mounted on oneof said cores, and means journalling said rotor only on said support inan overhanging position whereby said two-part housing can be separatedto provide access to said rotor while maintaining the support therefor.

2. The fluid flow meter according to claim 1 characterized in that theratio of the rotor blade chord length to blade spacing is in the orderof 1.1 to 1.5 at the mean radius of the blades and within such rangefrom the roots to the tips of the blades.

3. A fluid flow meter according to claim 1 characterized in that therotor blade chord length is larger at the rotor blade tips than at therotor blade roots and that the number of the blades on the rotor is inthe order of 12 to 24.

4. A fluid flow meter according to claim 1 characterized in that theblades of said rotor are soformed that the angle of attack of the fluidrelative to the blades is substantially uniform from the root to the tipof the leading edge of the blades.

5. A fluid flow meter according to claim 1 characterized in that theratio of the rotor blade chord length to blade chord spacing is in theorder of 1.5 at the roots of the blades and in the order of 1.2 at thetips of the blades.

6. A fluid flow meter according to claim 1 characterized in that theblades of the rotor are of lightweight thin air foil construction andhave a blade angle between 40 and with respect to the rotor rotationaxis.

7. A fluid flow meter according to claim 1 characterized in that theratio of the diameter of the inner boundary of said channel to thediameter of the outer boundary thereof is in the order of 0.60 to 0.85.

8. A fluid flow meter according to claim 1 characterized in that theblades of the rotor are straight in cylindrical cross section and theratio of the diameter of the inner boundary of the channel to thediameter of the outer boundary thereof is at least equal to 0.75.

9. A fluid flow meter according to claim 7 characterized in that in thecase of media of low inner friction, particularly gas, said diameterratio is in the range of 0.6 to 0.75.

10. A fluid flow meter according to claim 7 characterized in that in thecase of media of high inner friction said diameter ratio is in the rangeof 0.70 to 0.85.

11. The fluid flow meter defined in claim 1 wherein said rotor comprisesa hub having an appreciably smaller diameter than said cores and aplurality of spokes supporting said blades and extending radially fromsaid hub substantially to the inner diameter of said flow channel.

12. A fluid flowmeter comprising a housing, a rotatable rotor assemblydisposed in said housing and having a shaft and a peripherally bladedrotor carried by said shaft, means including a core structure fordirecting motive fluid into said rotor in an annular stream parallel tothe rotational axis of said rotor assembly for imparting drive torque tosaid rotor, means comprising axially spaced apart bearings supported bysaid core structure and journalling said shaft, said shaft having atleast a portion thereof formed from magnetic material and extendinggenerally horizontally in the normal operative position of said meter, amagnet supported by said core structure in radially spaced relationabove said magnetic portion of said shaft for applying a resultantmagnetic attractive force passing axially between said bearings andradially of said shaft to counterbalance the gravitational forces actingon said rotor assembly.

References Cited by the Examiner UNITED STATES PATENTS 789,110 5/05Warren 73231 1,967,449 7/34 Ostman 73-231 2,346,864 4/44 Packard 73-2292,449,973 9/48 Bergman 73-257 2,728,893 12/55 Bartelink 73231 X2,882,727 4/59 Newbold 73-231 2,974,525 3/61 Cole 73231 RICHARD C.QUEISSER, Primary Examiner. ROBERT L. EVANS, Examiner.

1. IN A FLUID FLOW METER, A SEPARABLE TWO-PART TUBULAR HOUSING HAVINGAXIALLY OPPOSED ABUTING SURFACES AND OPPOSITELY FACING ENDS PROVIDEDWITH MEANS ADAPTED TO ESTABLISH A CONNECTION TO A FLUID PIPELINE, A PAIROF AXIALLY SPACED APART, ALIGNED CORES COAXIALLY MOUNTED IN SAID HOUSINGAND DEFINING WITH THE INNER WALL OF SAID HOUSING A LONGITUDINAL FLUIDFLOW CHANNEL OF ANNULAR CROSS SECTION, AT LEAST THE UPSTREAM ONE OF SAIDCORES BEING FAIRED FOR GRADUALLY TRANSPOSING THE CROSS-SECTIONALCONFIGURATION OF THE ONCOMING FLUID STREAM, MEANS INDEPENDENTLY FIXINGSAID CORES TO RESPECTIVE ONES OF THE HOUSING PARTS, A ROTATABLE,PERIPHERAL BLADED METERING ROTOR DISPOSED AXIALLY BETWEEN SAID CORES ANDHAVING ITS BLADES IN THE PATH OF FLUID FLOWING THROUGH SAID CHANNEL TOBE DRIVEN BY FLUID FLOW THERETHROUGH, THE DOWNSTREAM ONE OF SAID CORESCOOPERATING WITH SAID HOUSING TO EXTEND SAID CHANNEL A PREDETERMINEDAXIAL DISTANCE DOWNSTREAM OF SAID ROTOR, SAID HOUSING PARTS ABUTTINGEACH OTHER ALONG ON INTERFACE CONTAINED IN A PLANE PASSING RADIALLYTHROUGH SAID ROTOR, A SUPPORT DETACHABLY MOUNTED ON ONE OF SAID CORES,AND MEANS JOURNALLING SAID ROTOR ONLY ON SAID SUPPORT IN AN OVERHANGINGPOSITION WHEREBY SAID TWO-PART HOUSING CAN BE SEPARATED TO PROVIDEACCESS TO SAID ROTOR WHILE MAINTAINING THE SUPPORT THEREFOR.